{"id":28,"date":"2010-01-25T22:20:24","date_gmt":"2010-01-25T22:20:24","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=28"},"modified":"2010-01-25T22:20:24","modified_gmt":"2010-01-25T22:20:24","slug":"update-2","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=28","title":{"rendered":"Update"},"content":{"rendered":"<p>In the discussion of groupoid stacks [U\/R] it turns out that given objects x, y of [U\/R] over some scheme T, then Isom(x, y) is fppf locally on T an algebraic space. Thus it makes sense to go back to algebraic spaces and prove a result characterizing algebraic spaces. Namely, an fppf sheaf of sets F for which there exists an algebraic space X and a map f : X &#8211;> F which is<\/p>\n<ul>\n<li>representable by algebraic spaces, and<\/li>\n<li>surjective, flat and locally of finite presentation<\/li>\n<\/ul>\n<p>is an algebraic space. The only ingredient missing for the proof is an analogue of Keel-Mori, Lemma 3.3. Hopefully we will have some time to write this in the near future.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the discussion of groupoid stacks [U\/R] it turns out that given objects x, y of [U\/R] over some scheme T, then Isom(x, y) is fppf locally on T an algebraic space. Thus it makes sense to go back to &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=28\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=28"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":32,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/28\/revisions\/32"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}